the lines of force of a magnetic field do not cross. why is this so
the magnetic field is single valued at a point in space it only has one value
QUESTION
The lines of force of a magnetic field do not cross each other because they are a representation of the direction and strength of the magnetic field at various points. These lines are continuous and form closed loops, known as magnetic field lines.
The reason why magnetic field lines do not cross is related to the fundamental behavior of magnetic fields, described by a property known as superposition. According to the principle of superposition, the magnetic field at any point is determined by the vector sum of the contributions from all individual magnets or current-carrying conductors in the vicinity.
If two magnetic field lines were to cross each other, it would imply that at that point, the magnetic field has two distinct and contradictory directions, which violates this principle. This would lead to ambiguity, making it challenging to determine the resultant magnetic field at that particular location.
Therefore, to maintain the consistency and clarity of the magnetic field representation, the lines of force are arranged in such a way that they never cross. They either run parallel to each other or curve around each other, allowing for a clear depiction of the magnetic field's direction and intensity at any given point.